van der Waals (vdW) heterostructures with two-dimensional (2D) crystals such as graphene, hexagonal boron nitride (hBN) and transition metal dichalcogenides (TMDCs) allow us to demonstrate atomically thin field-effect transistors (FETs), photodetectors (PDs) and photovoltaic devices capable of higher performance and greater stability levels than conventional devices. Although there have been studies of gas molecule sensing with 2D crystal channels, vdW heterostructures based on 2D crystals have not been employed thus far. Here, utilizing graphene/WS2/graphene (G/WS2/G) vdW heterostructure tunnel FETs, we demonstrate the rectification behavior of the sensitivity signal by tuning the WS2 potential barriers as a function of the gas molecule concentration and devise a fingerprint map of the sensitivity variation corresponding to an individual ratio of two different molecules in a gas mixture. Because the separation of different gas molecule concentrations from gas mixtures is in high demand in the gas-sensing research field, this result will greatly assist in the progress on selective gas sensing.